Yes, pretty sure AA fare rules only waives penalties (i.e., refundability) for death of traveler or companion, not a relative.
Changing the return after you've flown the outbound normally does not even require a re-faring if the same booking inventory is available (e.g., "I" class), however it sounds like the "$5000 if I return a day earlier" is either because (1) there's no I inventory on that day (which could easily appear, even on the day of departure), OR (2) because returning on that day does not meet the advance purchase requirements (e.g., 7 days, or Saturday night stay) of the fare. While it sounds like the issue is the former (because the $5k+ fare is both before and after the original travel date), if the issue is the latter, then they WILL re-price the return leg, and they might not be willing to grant an exception because that could be perceived as a loophole for business travelers. (Of course they could grant the exception with proof of death). And of course if the issue is booking class availability, they also may or may not be willing to open up the required fare class.

With travel insurance - make sure to read the terms of the policy, many will not reimburse for business class or there may be other $ limits.